I've tried to compile luasteam with SteamWorks v1.62, but it fails since SteamUserStats()->RequestCurrentStats() (in user_stats.cpp) no longer exists in this newer version of SteamWorks.

The isteamuserstats.h header has the following comment:

// Note: this call is no longer required as it is managed by the Steam client
// The game stats and achievements will be synchronized with Steam before
// the game process begins.

So that method is longer needed.

I resolved the issue by just removing the method from the module.
Later on I'll open a PR with this update.